The effect of viscous dissipation on the onset of convection in an inclined porous layer

2011 ◽  
Vol 679 ◽  
pp. 544-558 ◽  
Author(s):  
D. A. NIELD ◽  
A. BARLETTA ◽  
M. CELLI
Keyword(s):  
Viscous Dissipation ◽  
Lower Boundary ◽  
Boussinesq Approximation ◽  
Darcy Law ◽  
Convection Flow ◽  
Free Convection Flow ◽  
Onset Of Convection ◽  
Temperature Distributions ◽  
Residual Solution ◽  
Upper Boundary

The linear stability of a basic forced and free convection flow in an inclined porous channel is analysed by using the Darcy law and the Oberbeck–Boussinesq approximation. The basic velocity and temperature distributions are influenced by the effect of viscous dissipation, as well as by the boundary conditions. The boundary planes are assumed to be impermeable and isothermal, with a temperature of the lower boundary higher than that of the upper boundary. The instability against longitudinal rolls is studied by employing a second-order weighted residual solution and an accurate sixth-order Runge–Kutta solution of the disturbance equations. The instability against transverse rolls is also investigated. It is shown that these disturbances are in every case less unstable than the longitudinal rolls.

Transverse Heterogeneity Effects in the Dissipation-Induced Instability of a Horizontal Porous Layer

2011 ◽  
Vol 133 (12) ◽  
Author(s):  
A. Barletta ◽  
M. Celli ◽  
A. V. Kuznetsov
Keyword(s):  
Linear Stability ◽  
Porous Layer ◽  
Normal Modes ◽  
Lower Boundary ◽  
Boussinesq Approximation ◽  
Darcy Law ◽  
Main Task ◽  
Heterogeneity Effects ◽  
Upper Boundary

The linear stability of a parallel flow in a heterogeneous porous channel is analyzed by means of the Darcy law and the Oberbeck–Boussinesq approximation. The basic velocity and temperature distributions are influenced by the effect of the viscous dissipation, as well as, by the boundary conditions. A horizontal porous layer bounded by impermeable and infinitely wide walls is considered. The lower boundary is assumed to be thermally insulated, while the upper boundary is assumed to be isothermal. A transverse heterogeneity for the permeability and for the thermal conductivity is taken into account. The main task of this work is to investigate the role of this heterogeneity in changing the threshold for the onset of instability. A linear stability analysis by means of the normal modes method is performed. The onset of instability against oblique rolls is studied. The eigenvalue problem is solved numerically.

Second Grade Fluid for Rotating MHD of an Unsteady Free Convection Flow in a Porous Medium

2015 ◽  
Vol 362 ◽  
pp. 100-107 ◽  
Author(s):  
Z. Ismail ◽  
I. Khan ◽  
A.Q. Mohamad ◽  
S. Shafie
Keyword(s):  
Porous Medium ◽  
Free Convection ◽  
Initial Conditions ◽  
Boussinesq Approximation ◽  
Second Grade ◽  
Convection Flow ◽  
Inclined Plate ◽  
Free Convection Flow ◽  
Transform Method ◽  
The Laplace Transform

Rotating effects and magnetohydrodynamic (MHD) free convection flow of second grade fluids in a porous medium is considered in this paper. It is assumed that the bounding infinite inclined plate has ramped wall temperature with the presence of heat and mass diffusion. Based on Boussinesq approximation, the analytical expressions for dimensionless velocity, temperature and concentration are obtained by using the Laplace transform method. All the derived solutions satisfying the involved differential equations with imposed boundary and initial conditions. The influence of various parameters on the velocity has been analyzed in graphs and discussed.

scholarly journals Combined effect of conduction and viscous dissipation on magnetohydrodynamic free convection flow along a vertical flat plate

1970 ◽  
Vol 4 (2) ◽  
pp. 87-98 ◽  
Author(s):  
Abdullah Al-Mamun ◽  
Nur Hosain Md Ariful Azim ◽  
Md. Abdul Maleque
Keyword(s):  
Viscous Dissipation ◽  
Numerical Solutions ◽  
Transverse Magnetic ◽  
Convection Flow ◽  
Electrically Conducting ◽  
Temperature Distributions ◽  
Two Dimensional Flow ◽  
Marine Engineering ◽  
Energy Equations ◽  
Conjugate Conduction

This paper concerns the effects of conduction and viscous dissipation on natural convection flow of an incompressible, viscous and electrically conducting fluid in the presence of transverse magnetic field. Numerical solutions for the governing momentum and energy equations are given. A discussion has been provided for the effects of magnetic parameter, Prandtl number, conjugate conduction parameter and viscous dissipation parameter on two-dimensional flow. Results for the details of the velocity, temperature distributions as well as the skin friction and the rate of heat transfer are shown graphically. Also the numerical values of the surface temperature distributions are presented in tabular form.DOI: http://dx.doi.org/10.3329/jname.v4i2.992 Journal of Naval Architecture and Marine Engineering Vol.4(2) 2007 p.87-98

scholarly journals Viscous Dissipation and Dufour Effects on MHD Free Convection Flow Through an Oscillatory Inclined Porous Plate with Hall and Ion-Slip Current

2018 ◽  
Vol 7 (4.5) ◽  
pp. 410 ◽  
Author(s):  
K. V. B. Raja kumar ◽  
K. S. Balamurugan ◽  
Ch. V. Ramana Murthy ◽  
N. Ranganath
Keyword(s):  
Viscous Dissipation ◽  
Porous Plate ◽  
Convection Flow ◽  
Governing Equations ◽  
Inclined Plate ◽  
Regular Perturbation ◽  
Rotating System ◽  
Free Convection Flow ◽  
Ion Slip ◽  
Flow Through

In this paper the viscous dissipation and Dufour effects on Unsteady MHD free convective flow through a semi-infinite Oscillatory porous inclined plate of time dependent permeability with Chemical reaction and Hall and Ion-Slip Current in a Rotating System was investigated. The dimensionless governing equations for this investigation are solved analytically by using multiple regular perturbation law. The effects of different parameters on velocity, temperature and concentration fields are shown graphically.  

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